elliptic_integral
elliptic_integral,
an Octave code which
evaluates elliptic integral functions using Carlson's elliptic
functions.
The complete and incomplete elliptic functions of the first, second and
third kind can be evaluated, with parameters A (angle in degrees),
K (sine of A) or M (the modulus, K^2).
The Jacobi elliptic functions CN(U,M), DN(U,M) and SN(U,M) can be
evaluated with parameter M.
Licensing:
The computer code and data files made available on this web page
are distributed under
the MIT license
Languages:
elliptic_integral is available in
a C version and
a C++ version and
a Fortran77 version and
a Fortran90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
elliptic_integral_test
elfun,
an Octave code which
evaluates elliptic integrals and Jacobi elliptic functions cn(), dn(), sn(),
by Milan Batista.
ellipse,
an Octave code which
performs various geometric calculations for ellipses and ellipsoids.
test_values,
an Octave code which
supplies test values of various mathematical functions.
toms577,
an Octave code which
evaluates Carlson's elliptic integral functions RC, RD, RF and RJ.
This is a version of ACM TOMS algorithm 577;
Reference:
-
Roland Bulirsch,,
Numerical calculation of elliptic integrals and elliptic functions,,
Numerische Mathematik,,
Volume 7, Number 1, 1965, pages 78-90.
-
Bille Carlson,
Computing Elliptic Integrals by Duplication,
Numerische Mathematik,
Volume 33, 1979, pages 1-16.
-
Bille Carlson, Elaine Notis,
Algorithm 577, Algorithms for Incomplete Elliptic Integrals,
ACM Transactions on Mathematical Software,
Volume 7, Number 3, pages 398-403, September 1981.
Source Code:
-
elliptic_ea.m
evaluates the complete elliptic integral E(A).
-
elliptic_ea_values.m
returns values of the complete elliptic integral E(A).
-
elliptic_ek.m
evaluates the complete elliptic integral E(K).
-
elliptic_ek_values.m
returns values of the complete elliptic integral E(K).
-
elliptic_em.m
evaluates the complete elliptic integral E(M).
-
elliptic_em_values.m
returns values of the complete elliptic integral E(M).
-
elliptic_fa.m
evaluates the complete elliptic integral F(A).
-
elliptic_fa_values.m
returns values of the complete elliptic integral F(A).
-
elliptic_fk.m
evaluates the complete elliptic integral F(K).
-
elliptic_fk_values.m
returns values of the complete elliptic integral F(K).
-
elliptic_fm.m
evaluates the complete elliptic integral F(M).
-
elliptic_fm_values.m
returns values of the complete elliptic integral F(M).
-
elliptic_inc_ea.m
evaluates the incomplete elliptic integral E(PHI,A).
-
elliptic_inc_ek.m
evaluates the incomplete elliptic integral E(PHI,K).
-
elliptic_inc_em.m
evaluates the incomplete elliptic integral E(PHI,M).
-
elliptic_inc_fa.m
evaluates the incomplete elliptic integral F(PHI,A).
-
elliptic_inc_fk.m
evaluates the incomplete elliptic integral F(PHI,K).
-
elliptic_inc_fm.m
evaluates the incomplete elliptic integral F(PHI,M).
-
elliptic_inc_pia.m
evaluates the incomplete elliptic integral Pi(PHI,N,A).
-
elliptic_inc_pik.m
evaluates the incomplete elliptic integral Pi(PHI,N,K).
-
elliptic_inc_pim.m
evaluates the incomplete elliptic integral Pi(PHI,N,M).
-
elliptic_pia.m
evaluates the complete elliptic integral Pi(N,A).
-
elliptic_pia_values.m
returns values of the complete elliptic integral Pi(N,A).
-
elliptic_pik.m
evaluates the complete elliptic integral Pi(N,K).
-
elliptic_pik_values.m
returns values of the complete elliptic integral Pi(N,K).
-
elliptic_pim.m
evaluates the complete elliptic integral Pi(N,M).
-
elliptic_pim_values.m
returns values of the complete elliptic integral Pi(N,M).
-
jacobi_cnm.m
evaluates the Jacobi elliptic function CN(U,M).
-
jacobi_cn_values.m
returns some values of the Jacobi elliptic function CN(U,M).
-
jacobi_dnm.m
evaluates the Jacobi elliptic function DN(U,M).
-
jacobi_dn_values.m
returns some values of the Jacobi elliptic function DN(U,M).
-
jacobi_snm.m
evaluates the Jacobi elliptic function SN(U,M).
-
jacobi_sn_values.m
returns some values of the Jacobi elliptic function SN(U,M).
-
rc.m
computes the elementary integral RC(X,Y).
-
rd.m
computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
-
rf.m
computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
-
rj.m
computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
-
sncndn.m
evaluates the Jacobi elliptic functions SN(U,M), CN(U,M) and DN(U,M).
Last revised on 19 November 2020.